1 / 6

Circular Motion Example Problem 3: a t = f(t)

Circular Motion Example Problem 3: a t = f(t). A bead moves along a circular wire. Its speed increases at a = 2t – 4 m/s 2 . Its initial (at t = 0) position and speed are s(0) = 0 m and v(0) = 3 m/s. At t = 5 sec, please determine: (a) The magnitude of the bead’s acceleration.

roblesg
Download Presentation

Circular Motion Example Problem 3: a t = f(t)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Circular Motion Example Problem 3: at = f(t) A bead moves along a circular wire. Its speed increases at a = 2t – 4 m/s2. Its initial (at t = 0) position and speed are s(0) = 0 m and v(0) = 3 m/s. At t = 5 sec, please determine: (a) The magnitude of the bead’s acceleration. (b) The position of the bead along the wire (give both arc length, s, and angle, q. (c) The total distance traveled along the wire by the bead in the 0-5 sec time interval.

  2. Circular Motion Ex Prob 3: at = f(t) (a total dist problem) A bead moves along a circular wire. Its speed increases at a = 2t – 4 m/s2. Its initial (at t = 0) position and speed are s(0) = 0 m and v(0) = 3 m/s. At t = 5 sec, please determine… Solution: Step 1: Integrate the at function: Step 2: Evaluate at t = 5 sec

  3. Circular Motion Ex Prob 3: at = f(t) (a total dist problem) A bead moves along a circular wire. Its speed increases at a = 2t – 4 m/s2…. Step 3: Further investigate the bead’s motion… Find roots of the velocity equation…. v(t) = t2 – 4t + 3 m/s v = 0 = ( t – 1 )( t – 3 ) v = 0 at t = 1, 3 seconds Step 4: Evaluate s(t) at 0, 1, 3, 5 sec

  4. Circ Motion Ex Prob 3: at = f(t) (a total dist problem) Step 5: Plot the bead’s displacement along the wire…

  5. Circ Motion Ex Prob 3: at = f(t) (a total dist problem) Step 6: Bead’s position s (in meters) and q (in degrees) at t = 5 sec

  6. Circ Motion Ex Prob 3: at = f(t) (a total dist problem) Step 7: Acceleration magnitude at t = 5 sec

More Related